\begin{problem}{Self-Catalogue}{selfcatalogue.in}{selfcatalogue.out}{2 seconds}{}{}
 
     A self-catalogue is a sentence that truthfully and comprehensively 
     describes its own composition. In this problem, we are 
     concerned with sentences that count numerals occurring in themselves, 
     such as the following. 

\emph{This sentence contains 1 occurrence of 0, 2 occurrences of 1, 3 
occurrences of 2, and 2 occurrences of 3.}

The above is a self-catalogue because it gives an accurate count 
for each numeral occurring in itself. The following sentence, 
although accurate in the counts that it gives, is not a 
self-catalogue because it does not give a count for the numeral 3. 

\emph{This sentence contains 3 occurrences of 1, 1 
occurrence of 8, and 1 occurrence of 9.}

A self-catalogue must not give more than one count for the same 
numeral. Thus, the following is not a self-catalogue. 

\emph{This sentence contains 4 occurrences of 4, and 4 occurrences of 4.}

You will be given a count for each of the numeral 0 through 9. Try to 
find a self-catalogue that agrees with these counts. A 
count of 0 means that the numeral does not 
appear in the sentence at all, and a specified count of $-1$ means 
that any count (including 0) is acceptable. 

\InputFile

The input file contains ten counts for numerals from 0 to 9.
Each count is between $-1$ and 100, inclusive. 

\OutputFile

If there is no sentence meeting this specification, 
output \texttt{NO SOLUTION}.
Otherwise, you should output the solution 
in the same format as the input.
It must contain the same non-negative counts, but with each $-1$ 
replaced by an accurate count. If several self-catalogues are 
possible, choose the one that yields the smallest value in element 0 
of the result. If a tie remains, select for the 
smallest value in element 1; if there is still a tie, select for 
the smallest value in element 2; and so forth. 
Leading zeros are not permitted for any number appearing in a self-catalogue.


\Example

\begin{examplewide}
\exmp{        
1 -1 -1 -1 -1 -1 -1 -1 -1 -1
}{
1 2 3 2 0 0 0 0 0 0
}%
\exmp{
100 -1 -1 -1 -1 -1 -1 -1 -1 -1
}{
NO SOLUTION
}%
\exmp{
1 11 -1 -1 -1 -1 -1 -1 -1 -1
}{
1 11 0 1 1 1 1 1 1 1
}%
\exmp{
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1
}{
0 0 0 0 0 0 0 0 0 0
}% 
\end{examplewide}

\Note

The last self-catalogue illustrates this degenerate case:

\emph{This is a sentence.}

\end{problem}
 
 
 
